Thickness Dependence of Galvanomagnetic Properties in a Very Thin Slab

The thickness dependence of the magnetoresistance and the Hall constant is obtained in the twoband model with compensating charge carriers by using a specific perturbation formalism for quasitwo-dimensional systems. Screened impurity scattering is considered within the Boltzmann kinetic equation scheme, and the relaxation time is evaluated as a function of thickness through the scattering amplitude in the perturbation formulation. The relaxation time is not a simple linear function of thickness of the slab. The charge density and the effective masses are important parameters for the thickness dependence. The transport is also verified to be sensitive to the position of the impurity in the slab.